Gotabaye Rajapakse, secretary to the defence ministry and brother of President Mahinda Rajapakse, was unhurt after the blast in the heart of Colombo, they said.
Fourteen people were hurt, most of them security personnel.
The secretary was travelling to a security council meeting with the president at the official Temple Trees executive residence, a source at the president's office told AFP.
"The defence secretary was in the convoy, he was unhurt. He drove straight to Temple Trees and the first thing he did was to hug the president," said the source who asked not to be named.
Police said the suicide bomber rammed a three-wheel rickshaw taxi into the convoy of some eight vehicles.
The defence secretary was inside a bullet-proof vehicle, police said.
The Liberation Tigers of Tamil Eelam (LTTE) have been fighting for a separate state for Sri Lanka's 2.5 million Tamil minority for three decades in a conflict that has left more than 60,000 people dead.
The LTTE has carried out regular suicide attacks on government and civilian targets.

Gotabaye Rajapakse, secretary to the defence ministry and brother of President Mahinda Rajapakse, was unhurt after the blast in the heart of Colombo, they said.
Fourteen people were hurt, most of them security personnel.
The secretary was travelling to a security council meeting with the president at the official Temple Trees executive residence, a source at the president's office told AFP.
"The defence secretary was in the convoy, he was unhurt. He drove straight to Temple Trees and the first thing he did was to hug the president," said the source who asked not to be named.
Police said the suicide bomber rammed a three-wheel rickshaw taxi into the convoy of some eight vehicles.
The defence secretary was inside a bullet-proof vehicle, police said.
The Liberation Tigers of Tamil Eelam (LTTE) have been fighting for a separate state for Sri Lanka's 2.5 million Tamil minority for three decades in a conflict that has left more than 60,000 people dead.
The LTTE has carried out regular suicide attacks on government and civilian targets.